3. Digit recognition
Classification is an supervised learning task by which we aim to
predict the correct label for an example given its features
↓
0 5 4 1 4 9
e.g. determine which digit {0, 1, . . . , 9} is in depicted in each
image
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 3 / 23
4. Digit recognition
Determine which digit {0, 1, . . . , 9} is in depicted in each image
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 4 / 23
5. Images as arrays
Grayscale images ↔ 2-d arrays of M × N pixel intensities
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 5 / 23
6. Images as arrays
Grayscale images ↔ 2-d arrays of M × N pixel intensities
Represent each image as a “vector of pixels”, flattening the 2-d
array of pixels to a 1-d vector
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 5 / 23
7. k-nearest neighbors classification
k-nearest neighbors: memorize training examples, predict labels
using labels of the k closest training points
Intuition: nearby points have similar labels
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8. k-nearest neighbors classification
Small k gives a complex boundary, large k results in coarse
averaging
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 7 / 23
9. k-nearest neighbors classification
Evaluate performance on a held-out test set to assess
generalization error
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 7 / 23
12. Image classification
Determine if an image is a landscape or headshot
↓ ↓
’landscape’ ’headshot’
Represent each image with a binned RGB intensity histogram
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 10 / 23
13. Images as arrays
Color images ↔ 3-d arrays of M × N × 3 RGB pixel intensities
import matplotlib . image as mpimg
I = mpimg . imread ( ' chairs . jpg ')
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 11 / 23
14. Images as arrays
Color images ↔ 3-d arrays of M × N × 3 RGB pixel intensities
import matplotlib . image as mpimg
I = mpimg . imread ( ' chairs . jpg ')
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 11 / 23
15. Intensity histograms
Disregard all spatial information, simply count pixels by intensities
(e.g. lots of pixels with bright green and dark blue)
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16. Intensity histograms
How many bins for pixel intensities?
Too many bins gives a noisy, overly complex representation of
the data,
while using too few bins results in an overly simple one
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 13 / 23
17. Image classification
Classify
./ classify_flickr . py 16 9
flickr_headshot flickr_landscape
Change in performance on test set with number of neighbors
k = 1, accuracy = 0.7125
k = 3, accuracy = 0.7425
k = 5, accuracy = 0.7725
k = 7, accuracy = 0.7650
k = 9, accuracy = 0.7500
Jake Hofman (Columbia University) Data-driven modeling January 30, 2012 14 / 23
